Problem 1106. I've got the power! (Inspired by Project Euler problem 29)

Created by James
Appears in Project Euler III

Difficulty:Rate

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Consider all integer combinations of a^b and b^a for the integer values 2 ≤ a ≤ 4 and 2 ≤ b ≤ 5:

    2^2=4,  2^3=8,   2^4=16,  2^5=32
    3^2=9,  3^3=27,  3^4=81,  3^5=243
    4^2=16, 4^3=64,  4^4=256, 4^5=1024
    5^2=25, 5^3=125, 5^4=625

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 14 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024

Given two values for x and y, find the unique, sorted sequence given by the values a^b and b^a for 2≤a≤x and 2≤b≤y.

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343 Solutions
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Last Solution submitted on Mar 11, 2025

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3 Comments

@bmtran (Bryant Tran) on 7 Dec 2012

What your problem description asks for and what your test suite asks for are different. Specifically, test case 4 requires that the operation be commutative, which, by your problem statement, it is not (since the power function itself is not commutative). This is reflected in the other test cases as well. (also, you call your arguments x and y in the description and a and b in the template).

James on 7 Dec 2012

You are correct. I had the "and b^a" in there originally, but I accidentally deleted it when I added the "for 2≤a≤x and 2≤b≤y" text. It's fixed now, and the description should be a bit clearer.

@bmtran (Bryant Tran) on 7 Dec 2012

thanks James!

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Project Euler III

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